Boundary Compensation – Compensated Islands III: Certified Transport Atlases and Reset Obstructions over Parameter Bases

This paper develops the third module of the Compensated Islands branch of the BoundaryCompensation programme. BC-CI-I introduced finite-dimensional near-compensated residuallayers generated by mapsLθ = P(IK + Kθ), Bθ = LθL∗θ,with a nonzero but bounded observed residual. BC-CI-II introduced certified residualtransport along a declared parameter pathγ : [0, 1] → Θ,where propagation means certified continuation of a readout channel, not physical timeevolution. The present paper lifts that pathwise construction to a multi-chart parameter base.It defines finite-dimensional certified transport charts, overlap transition certificates, gluingcompatibility, and reset obstructions for families of response operators over a parameterregionM ⊆ Θ.The central object is a certified transport atlasA = {Ci}i∈I ,where each chart carries local channel labels, spectral or declared readout projectors, rankdata, cluster-accessibility margins, and readout-status information. On overlaps, localchannel labels are compared by partial transition maps. A gluing certificate is not assumedautomatically: it requires compatible ranks, controlled projector mismatch, positive thresholdmargins, and bounded triple-transition defect. If an overlap or triple-overlap condition fails,the status is a reset obstruction rather than a physical singularity, causal horizon, gaugecurvature, or Berry phase.The paper proves elementary finite-dimensional facts: positive margins yield local transport charts; overlap certificates are stable under sufficiently small deterministic perturbations;pathwise certified transport can be recovered by walking through a gluable atlas; and localchannel certificates do not imply a global channel unless overlap and triple compatibilityare certified. The contribution is architectural and certification-theoretic. It provides theatlas layer needed before any future attempt to interpret residual transport as effectivecausal order, field-like propagation, or horizon-like failure. No spacetime geometry, physicaldynamics, Hamiltonian, quantum field, photon, gauge field, Berry phase, holonomy, orempirical prediction is claimed.